Convert Degrees, Minutes, Seconds to Decimal Degrees 41 degrees 36'40''

$41 ° 36' 40''$

Since $41$ is a whole number, it is a full degree. Since each minute is equal to $\frac{1}{60}$ degree, multiply $36$ by $\frac{1}{60}$ . Since each second is equal to $\frac{1}{3600}$ degree, multiply $40$ by $\frac{1}{3600}$ . Add them together.

$41 + 36 \cdot \frac{1}{60} + 40 \cdot \frac{1}{3600}$

Simplify.

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Remove parentheses.

$41 + 36 \cdot \frac{1}{60} + 40 \cdot \frac{1}{3600}$

Simplify each term.

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Cancel the common factor of $12$ .

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Factor $12$ out of $36$ .

$41 + 12 (3) \cdot \frac{1}{60} + 40 \cdot \frac{1}{3600}$

Factor $12$ out of $60$ .

$41 + 12 \cdot 3 \cdot \frac{1}{12 \cdot 5} + 40 \cdot \frac{1}{3600}$

Cancel the common factor.

$41 + 12 \cdot 3 \cdot \frac{1}{12 \cdot 5} + 40 \cdot \frac{1}{3600}$

Rewrite the expression.

$41 + 3 \cdot \frac{1}{5} + 40 \cdot \frac{1}{3600}$

Combine $3$ and $\frac{1}{5}$ .

$41 + \frac{3}{5} + 40 \cdot \frac{1}{3600}$

Cancel the common factor of $40$ .

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Factor $40$ out of $3600$ .

$41 + \frac{3}{5} + 40 \cdot \frac{1}{40 (90)}$

Cancel the common factor.

$41 + \frac{3}{5} + 40 \cdot \frac{1}{40 \cdot 90}$

Rewrite the expression.

$41 + \frac{3}{5} + \frac{1}{90}$

Find the common denominator.

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Write $41$ as a fraction with denominator $1$ .

$\frac{41}{1} + \frac{3}{5} + \frac{1}{90}$

Multiply $\frac{41}{1}$ by $\frac{90}{90}$ .

$\frac{41}{1} \cdot \frac{90}{90} + \frac{3}{5} + \frac{1}{90}$

Multiply $\frac{41}{1}$ and $\frac{90}{90}$ .

$\frac{41 \cdot 90}{90} + \frac{3}{5} + \frac{1}{90}$

Multiply $\frac{3}{5}$ by $\frac{18}{18}$ .

$\frac{41 \cdot 90}{90} + \frac{3}{5} \cdot \frac{18}{18} + \frac{1}{90}$

Combine.

$\frac{41 \cdot 90}{90} + \frac{3 \cdot 18}{5 \cdot 18} + \frac{1}{90}$

Multiply $5$ by $18$ .

$\frac{41 \cdot 90}{90} + \frac{3 \cdot 18}{90} + \frac{1}{90}$

Combine fractions.

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Combine fractions with similar denominators.

$\frac{41 \cdot 90 + 3 \cdot 18 + 1}{90}$

Multiply.

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Multiply $41$ by $90$ .

$\frac{3690 + 3 \cdot 18 + 1}{90}$

Multiply $3$ by $18$ .

$\frac{3690 + 54 + 1}{90}$

Simplify the numerator.

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Add $3690$ and $54$ .

$\frac{3744 + 1}{90}$

Add $3744$ and $1$ .

$\frac{3745}{90}$

Cancel the common factor of $3745$ and $90$ .

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Factor $5$ out of $3745$ .

$\frac{5 (749)}{90}$

Cancel the common factors.

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Factor $5$ out of $90$ .

$\frac{5 \cdot 749}{5 \cdot 18}$

Cancel the common factor.

$\frac{5 \cdot 749}{5 \cdot 18}$

Rewrite the expression.

$\frac{749}{18}$

Convert the fraction to a decimal by dividing the numerator by the denominator.

$41.6\overline{1} °$

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